Airfare is at all-time highs this year and I don't see any significant signs of it coming down soon. As others have said, use Google Flights to see what a good price is estimated to be. I fly almost exclusively Delta. For the flights I watch on Delta, I usually see prices start out on the lower price end, go up after a couple of weeks and sit there for several months, then come back down (sometimes lower that the release prices, but not always), then slowly climb as the fight approaches and fills up. I tend to book when flights are released and get an e-credit if they drop in price, but you are past that window now.
I wouldn't do a connection from NYC unless it saves you a lot of money. It can be really easy or really hard, depending on your luck. We connected through Amsterdam last year and the workers went on strike weeks before we flew and it caused major disruptions. Things cleared up days before our flight, but it was a stress point. The layover there was also long and was just another exposure point for COVID as there seemed to be so many sick people packed together. Not to mention, connections are always an additional complication if flights are delayed. I would pay a premium for a direct flight, assuming it was in my budget.
I highly recommend traveling carryon only to Europe. Four families on our cruise had their luggage lost by Delta and were winging it. I have had multiple family members also not have there luggage make it to Europe on various airlines. Almost all of the frequent travelers I know only do carryon to Europe from the U.S. If you do decide to check, make sure you at least carry on a small bag with essentials, a change of clothes, and anything you can't live without on the cruise that would be hard to replace quickly in Europe.
